Method of measuring unsaturated inductances of an equivalent circuit of a synchronous machine

ABSTRACT

Unsaturated inductances of an equivalent circuit of a synchronous machine are measured from the following steps: An armature resistance of a synchronous machine is measured. A time constant of an armature with damper under a quadrature-axis magnetomotive force is measured when an armature and a field are in a positional relationship wherein a magnetomotive force by flowing current to an armature coil of the synchronous machine becomes the quadrature-axis magnetomotive force. Also, a current and a voltage of the armature are measured when the armature and the field are in the positional relationship by a quadrature-axis Dalton-Cameron method. The measured values are then used for solving equations defining inductances of a quadrature-axis equivalent circuit of the synchronous machine.

This application is a divisional of application Ser. No. 07/928,347,filed Aug. 12, 1992, now U.S. Pat. No. 5,309,089, issued on May 3, 1994.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a method of measuring unsaturated inductancesof an equivalent circuit of a synchronous machine for obtainingunsaturated values of inductances in the equivalent circuit of asynchronous machine.

2. Discussion of Background

A synchronous machine is mainly utilized as a generator or a motoralways running at a predetermined revolution number. Reactances in thesemachines are generally utilized for calculating a limit of an output, astability or the like. Accordingly, an inductance (inductance multipliedby 2πf is reactance) treated as a value viewed from an armature such asa synchronous reactance or a transient reactance, attracts attention.

For instance, various test methods are described in "the Abstract ofTest Methods for a Synchronous Machine (Parts 1 to 4)" (issued by theInstitute of Electrical Engineers of Japan) summarizing test methods ofthe synchronous machine, for measuring inductances of the synchronousmachine. However, no description is found in the abstract concerning amethod of measuring values of elements constituting an equivalentcircuit of the synchronous machine, such as an armature leakageinductance, a field leakage inductance, a direct-axis damper leakageinductance, a direct-axis armature reaction inductance, aquadrature-axis damper leakage inductance and a quadrature-axis armaturereaction inductance, based on a unified theory.

Accordingly, these values are obtained by combining known methods, whenthe values of the respective elements constituting the equivalentcircuit of the synchronous machine are necessary. For instance, onemethod is as follows.

First, a direct-axis synchronous reactance is obtained based on resultsof a no-load saturation characteristic test and a three-phaseshort-circuit characteristic test. The direct-axis armature reactionreactance is determined by subtracting a value of the armature leakagereactance from the above value. In this occasion, an assumed value isoften adopted as the value of the armature leakage reactance. Toactually measure the armature leakage reactance, it is necessary to drawout a rotor thereof and provide additional wirings, which requiresconsiderable time and labor.

Next, a direct-axis transient reactance is obtained by a three-phasesudden short-circuit test. A parallel value of the direct-axis armaturereaction reactance and the field leakage reactance is obtained by theabove value substracted by the value of the armature leakage reactance.Furthermore, the field leakage reactance is separated from the parallelvalue.

Similarly, a direct-axis initial transient reactance is obtained by thethree-phase sudden short-circuit test. A parallel value of thedirect-axis armature reaction reactance, the field leakage reactance andthe direct-axis damper leakage reactance is obtained by subtracting thevalue of the armature leakage reactance from the above value.Furthermore, the direct-axis damper leakage reactance is separated fromthe parallel value.

The respective reactances concerning the quadrature-axis, are obtainedas follows. First, a quadrature-axis synchronous reactance is obtainedby a measurement result by the slip method. The quadrature-axis armaturereaction reactance is determined by subtracting the value of thearmature leakage reactance from the above value.

Next, a quadrature-axis initial transient reactance is obtained by ameasurement result by Dalton-Cameron method. A parallel value of thequadrature-axis armature reaction reactance and a quadrature-axis damperleakage reactance is obtained by subtracting the value of the armatureleakage reactance from the above value. Furthermore, the quadrature-axisleakage reactance is separated from the parallel value.

In the meantime, there is a vector control capable of controlling withhigh accuracy, as a control method of the synchronous machine. Toperform the vector control, it is necessary to set detailed values ofthe respective elements constituting the equivalent circuit of thesynchronous machine to a control device, as motor constants.Accordingly, in cases of driving the synchronous machine by the vectorcontrol, the respective reactance values has previously been obtained bythe above method, which are set to the control device.

Since the method of measuring unsaturated inductances of the equivalentcircuit of the synchronous machine, is as above, the high accuracy ofthe respective reactance values can not be expected. That is, the abovemethod is a combination of available measuring methods such as inmeasuring the no-load saturation characteristic, which is not a methodbased on a unified theory. Accordingly, it is impossible to investigateinfluence of the respective values on a total measurement accuracy.

Furthermore, since the actual measurement of the armature leakagereactance is not easy, an assumed value is apt to be adopted as thevalue, which causes lowering of the measurement accuracy. Furthermore,the synchronous machine having a large capacity controlled by the vectorcontrol, is often driven at a rated frequency of about 2 to 10 Hz. Incase of such a low rated frequency, as a result of the three-phasesudden short-circuit test, a number of waves contained in a waveformbecomes less, and it becomes difficult to read the direct-axis transientreactance and the direct-axis initial transient reactance from thewaveform.

Furthermore, to carry out the slip method test, it is necessary to drivethe rotor at a speed slightly different from a speed of a revolvingfield of a stator. Accordingly, when a size of the synchronous machinewhich is an object of the test, is enlarged, a three-phase power sourceon the side of the stator, a driving motor on the side of the rotor andthe like become large-scale ones. In performing the test, a skilleddriving operation is required to stably maintain a low slip. A pulsationin a revolution number caused by an influence of a reaction torque, or atoo much slip causes measurement errors.

In the conventional method stated as above, there is a high possibilityof containing errors in the measurement values. Furthermore, much laborand time are required in the measurement.

When the motor constants of the control device in the vector control,are to be set, optimum values should be set since the set valuesconsiderably influence on accuracy of a control calculation. Since theaccuracy of the measurement value by the above method, is poor, anoperation of setting optimum motor constants by repeating a drivingoperation wherein the control device and the synchronous machine arecombined, is required. The time and the expense required for theoperation are enormous in case of a large capacity machine.

SUMMARY OF TEE INVENTION

It is an object of the present invention to solve the above problems. Itis an object of the present invention to provide a method of measuringunsaturated inductances of an equivalent circuit of a synchronousmachine capable of accurately obtaining the unsaturated values ofinductances of respective elements constituting the equivalent circuit,and as a result, capable of determining the motor constants to be givento the control device of the vector control by a single body test of thesynchronous machine.

According to a first aspect of the present invention, there is provideda method of measuring unsaturated inductances of an equivalent circuitof a synchronous machine comprising:

measuring a no-load saturation characteristic of a synchronous machine;

measuring a three-phase short-circuit characteristic of the synchronousmachine;

measuring currents and voltages of an armature and a field when anarmature coil and a field coil are in a positional relationship whereina magnetomotive force by flowing current to the armature coil of thesynchronous machine becomes a direct-axis magnetomotive force and bothwhen the field coil is in an open-circuit state and when the field coilis in a short-circuit state by direct-axis Dalton-Cameron method; and

solving simultaneous equations concerning a direct-axis equivalentcircuit of the synchronous machine by using results of the measuring theno-load saturation characteristic, the measuring the three-phaseshort-circuit characteristic and the measuring by the direct-axisDalton-Cameron method, thereby obtaining impedances of respectiveelements constituting the direct-axis equivalent circuit.

According to a second aspect of the present invention, there is provideda method of measuring unsaturated inductances of an equivalent circuitof a synchronous machine comprising:

measuring an armature resistance of a synchronous machine;

measuring a time constant of an armature with damper under aquadrature-axis magnetomotive force when an armature and a field is in apositional relationship wherein a magnetomotive force by flowing currentto an armature coil of the synchronous machine becomes thequadrature-axis magnetomotive force;

measuring a current and a voltage of the armature when the armature andthe field are in said positional relationship by a quadrature-axisDalton-Cameron method;

solving calculating equations concerning a quadrature-axis equivalentcircuit of the synchronous machine by using results of the measuring thearmature resistance, the measuring the time constant of the armaturewith damper under the quadrature-axis magnetomotive force and themeasuring by the quadrature-axis Dalton-Cameron method, therebyobtaining inductances of respective elements constituting thequadrature-axis equivalent circuit.

The respective measuring steps in the first aspect of the presentinvention, can be performed in a steady state, that is, without readingtimewisely variable data. Therefore, a possibility of containing errorsin the measurement result is reduced. The measuring steps by thedirect-axis Dalton-Cameron method can be performed in a stationary stateof the synchronous machine. The performing difficulty is inconsiderableand the measurement error due to a variation in the revolution numberand an error in the revolution number, are avoided.

Furthermore, in the respective measuring steps in the second aspect ofthe present invention, it is possible to perform the measurements at astationary state of the synchronous machine, thereby avoiding themeasurement error due to a variation in the revolution number and anerror in the revolution number.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the invention and many of the attendantadvantages thereof will be readily obtained as the same becomes betterunderstood by reference to the following detailed description whenconsidered in connection with the accompanying drawings, wherein:

FIG. 1 is an explanatory diagram showing a total flow of a method ofobtaining inductances of respective elements constituting a direct-axisequivalent circuit and a quadrature-axis equivalent circuit;

FIG. 2 is a circuit diagram showing a measurement circuit for measuringa no-load saturation characteristic;

FIG. 3 is a characteristic diagram showing the no-load saturationcharacteristic;

FIG. 4 is a circuit diagram showing a measurement circuit for measuringa three-phase short-circuit characteristic;

FIG. 5 is a circuit diagram showing a circuit for preparing to perform adirect-axis Dalton-Cameron method;

FIG. 6 is a circuit diagram showing a measurement circuit by thedirect-axis Dalton-Cameron method under a condition of open-circuit of afield coil;

FIG. 7 is a circuit diagram showing a measurement circuit for measuringby the direct-axis Dalton-Cameron method under a condition ofshort-circuit of the field coil;

FIG. 8 is an explanatory diagram showing measurement items with therespect to the direct-axis;

FIG. 9 is an explanatory diagram showing a direct-axis equivalentcircuit of the synchronous machine;

FIG. 10 is a circuit diagram for showing a circuit for preparing tomeasure a time constant of a quadrature-axis armature with damper and toperform a quadrature-axis Dalton-Cameron method;

FIG. 11 is an explanatory diagram showing a positional relationshipbetween an armature and a rotor;

FIG. 12 is a circuit diagram showing a measurement circuit for measuringan armature resistance and a time constant of a quadrature-axis armaturewith damper;

FIG. 13 is a waveform diagram showing a waveform of an armature currentwhen the time constant of the quadrature-axis armature with damper, ismeasured;

FIG. 14 is a circuit diagram showing a measurement circuit by thequaderature-axis Dalton-Cameron method;

FIG. 15 is an explanatory diagram showing measurement items with respectto the quadrature-axis; and

FIG. 16 is an explanatory diagram showing a quadrature-axis equivalentcircuit of the synchronous machine.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS EXAMPLE 1

Explanation will be given to an embodiment of the present invention asfollows.

FIG. 1 is an explanatory diagram showing a total flow of a method ofobtaining inductances of respective elements constituting a direct-axisequivalent circuit and a quadrature-axis equivalent circuit.

FIG. 1 shows that values of the inductances of the respective elementsconstituting a direct-axis equivalent circuit can be obtained bymeasuring a no-load saturation characteristic, measuring a three-phaseshort-circuit characteristic, measuring by a direct-axis Dalton-Cameronmethod under a condition of open-circuit of a field and measuring by thedirect-axis Dalton-Cameron method under a condition of short-circuit ofthe field, and by solving simultaneous equations concerning thedirect-axis equivalent circuit.

Furthermore, FIG. 1 shows that values of inductances of respectiveelements constituting a quadrature-axis equivalent circuit can beobtained, by measuring an armature resistance, measuring a time constantof the quadrature-axis armature with damper, measuring byquadrature-axis Dalton-Cameron method, and by solving calculatingequations concerning the quadrature-axis equivalent circuit.

In this specification, the "armature with damper" signifies that adamper is magnetically coupled with the armature. In the quadrature-axisequivalent circuit, the damper is parallelly connected to thequadrature-axis armature reaction inductance L_(aq).

Next, explanation will be given to the measurement of the inductancesconcerning the direct-axis equivalent circuit referring to the drawings.FIG. 2 shows a measurement situation of the no-load saturationcharacteristic. In FIG. 2, a reference numeral 1 designates an armaturecoil, 2, a rotor (field), 3, a field coil, 10, a direct current powersource, 11, an ammeter (D.C.) connected to the field coil 3, and 32, analternating current voltmeter connected between the "b" phase and the"c" phase of the armature coil 1.

In this case, the rotor 2 is driven at a constant speed, normally at arated revolution number of the synchronous machine. Under the condition,a line voltage V_(bc0) which is induced in the armature coil 1 in anopen-circuit state by excitation by a field current I_(f0), and afrequency f₀ are measured respectively by the alternating currentvoltmeter 32 and a frequency indicator (not shown) (refer to FIG. 8).FIG. 3 shows a no-load saturation characteristic. In this case,unsaturated values of the line voltage V_(bc0) and the field currentI_(f0) are adopted in a range wherein the characteristic is regarded asapproximately linear.

FIG. 4 shows a measurement situation of the three-phase short-circuitcharacteristic. In FIG. 4, a reference numeral 31 designates analternating current ammeter connected among the "b" phase, the "c" phaseand the "a" phase of the armature coil 1. In this case, the rotor 2 isdriven at a constant speed, normally at a rated revolution number of thesynchronous machine. Under the condition, a current I_(as) which isinduced in the armature coil 1 in a short-circuit state by excitation bya field current I_(fs), is measured (refer to FIG. 8).

FIG. 5 shows a situation of preparing to perform the direct-axisDalton-Cameron method. In this case, a direct current flows from the "b"phase to the "c" phase of the armature coil 1 by a direct current powersource 20. At the same time, a direct current flows in the field coil 3.Then, the rotor 2 rotates to a position wherein the stator and the rotor2 pull together by a magnetic force, and is fixed there. That is, therotor 2 is fixed to a position, for instance, shown in FIGS. 6 and 7.

When the rotor 2 is situated at the position shown in FIGS. 6 and 7, andwhen a current flows from the "b" phase to the "c" phase of the armaturecoil 1, a magnetomotive force by the current flowing is a direct-axismagnetomotive force. Accordingly, as shown in FIG. 5, when currentsstart flowing in the armature coil 1 and the field coil 2, and when itis confirmed that the rotor 2 strongly rotates to the stable positionshown in FIGS. 6 and 7, a current flows from the "b" phase to the "c"phase in a stationally state of the rotor. In this way, values withrespect to the direct-axis are measured wherein they are clearlydefined, which is different from the conventional measurement by theDalton-Cameron method performed at an arbitral position of the rotor.

FIG. 6 shows a measurement situation under a condition of open-circuitof the field coil 3. That is, an alternating current having frequency off₁ flows from the "b" phase to the "c" phase of the armature coil 1 byan alternating current power source 30. A current I_(bc1) flowing fromthe "b" phase to the "c" phase, a voltage V_(bc1) between the "b" phaseand the "c" phase and a voltage V_(f1) induced in the field coil 3 arerespectively measured by the alternating current ammeter 31, thealternating current voltmeter 32 and an alternating current voltmeter 12(refer to FIG. 8).

FIG. 7 shows a measurement situation under a condition wherein the fieldcoil 3 is shortcircuited. That is, an alternating current flows from the"b" phase to the "c" phase of the armature coil 1. A current I_(bc2)flowing from the b phase to the "c" phase and a current I_(f2) inducedin the field coil 3 are respectively measured by the alternating currentammeter 31 and an ammeter (A.C.) 11 (refer to FIG. 8).

In these measurements by the direct-axis Dalton-Cameron method, it ispreferable to utilize 50 Hz or 60 Hz as the frequency f₁ in a largecapacity machine. However, the frequency may be chosen in a range of 10to 100 Hz. The currents I_(bc1) and I_(bc2) flowing between the "b"phase and the "c" phase of the armature coil 1 are preferable to beabout 10 to 20% of the rated current value. FIG. 8 summarizesmeasurement items and utilized measuring instruments with respect to theabove-mentioned measurements. An order of the above-mentioned four itemsof the measurements can arbitrarily be chosen.

FIG. 9 shows an equivalent circuit of the synchronous machine when therotor 2 is at the position shown in FIGS. 6 and 7. When the equivalentcircuit is to be represented by equations, the following simultaneousequations are obtained. ##EQU1##

By inputting the measurement results shown in FIG. 8 into thesimultaneous equations, and by solving with respect to the unknown, fourdirect-axis unsaturated inductances, that is, the armature leakageinductance L_(l), the field leakage inductance L_(f), the direct-axisdamper leakage inductance L_(kd) and the direct-axis armature reactioninductance L_(ad), and a turn ratio T_(r) between the equivalent circuitand the actual field coil 3, can be obtained.

The simultaneous equations can be solved by a numerical calculationmethod. For instance, by using Gauss-Seidel iteration method, thecalculation converges by iterations of about five times.

EXAMPLE 2

Next, explanation will be given to the measurement of inductances withrespect to the quadrature-axis equivalent circuit referring to thedrawings. FIG. 10 shows a situation of preparing to perform measurementsof a time constant of the quadrature-axis armature with damper and bythe quadrature-axis Dalton-Cameron method. In this case, the "b" phaseand the "c" phase of the armature coil 1 are shortcircuited, and adirect current flows from the "a" phase to the "b" phase and the "c"phase by a direct current power source 40. At the same time, a directcurrent flows in the field coil 3.

Then, the rotor 2 rotates to a position wherein the stator and the rotor2 pull together, and fixed there. That is, the rotor 2 is fixed to, forinstance, a position shown in FIG. 11. When a current flows from the "a"phase to the "b" phase and the "c" phase of the armature coil 1, whilethe rotor 2 stays at that position, the magnetomotive force by thecurrent flowing is a direct-axis magnetomotive force. On the contrary,when a current flows from the "b" phase to the "c" phase, themagnetomotive force by the current flowing is a quadrature-axismagnetomotive force.

Accordingly, when it is confirmed that currents start flowing in thearmature coil 1 and the field coil 2 as shown in FIG. 10, and the rotor2 strongly rotates and stops at a stable position shown in FIG. 11, acurrent is to flow from the "b" phase to the "c" phase in a stationarystate of the rotor. In this way, the measurement of the inductances withrespect to the quadrature-axis becomes possible.

FIG. 12 shows a situation wherein a current flows from the "b" phase tothe "c" phase of the armature coil 1 by opening a switch 24. In thissituation, a current I_(bc) flowing from the "b" phase to the "c" phaseand a voltage V_(bc) between the "b" phase and the "c" phase arerespectively measured by a direct current ammeter 21 and a directcurrent voltmeter 22 (refer to FIG. 15). Accordingly, an armatureresistance R_(bc) can be determined by the following equation. ##EQU2##

Next, when a situation shown in FIG. 12, that is, the situation whereina current flows from the "b" phase to the "c" phase, is changed to asituation wherein the "b" phase and the "c" phase are shortcircuited byclosing the switch 24, the current I_(bc) recirculates in the armaturecoil 1 and attenuates by the armature resistance and by an influence ofa quadrature-axis damping effect. FIG. 13 shows an actually measuredwaveform of the current I_(bc) by an oscilloscope. By the way, aresistance 23 connected in series to the direct current power source 20in FIG. 12, designates a protection resistance for preventing the directcurrent power source 20 from the short-circuit when the switch 24 isclosed, and for short-circuiting only the armature coil.

As shown in FIG. 13, the current I_(bc) rapidly falls just after theshort-circuit, and gradually attenuates. At this occasion, a timeconstant of the armature with damper is measured by a time T_(e1)wherein the current I_(bc) attenuates to I_(e1), 30% of an initial valueI_(b0) (refer to FIG. 15). The time constant normally designates a timefor the current I_(bc) to attenuates to 1/e=0.37 of the initial valueI_(b0). However, in this measurement, the time for the current toattenuate to 0.3 of the initial value, is utilized.

The value of 0.3 is determined based on results of various experimentsand simulations performed to investigate the influence of thequadrature-axis damping effect, and is an optimum value for obtainingthe time constant of the quadrature-axis armature circuit which removesan influence of the quadrature-axis damper. Since the time for thecurrent I_(bc) to become I_(e1) (=0.3I_(b0)) is measured, actually, -log(I_(e1) /I_(b0))=-log (0.3) =1.2 times of the time constant T_(adq) ofthe quadrature-axis armature circuit is measured as T_(e1). However,this point is considered in the equations mentioned later.

FIG. 14 shows a situation of the measurement by the guadrature-axisDalton-Cameron method. In this case, an alternating current havingfrequency of f₃ flows between the "b" phase and the "c" phase of thearmature coil from the alternating current power source 30. A currentI_(bc3) and a voltage V_(bc3) are measured (refer to FIG. 15).

In this measurement by the quadrature-axis Dalton-Cameron method, it ispreferable to utilize 50 Hz or 60 Hz as the frequency f₃ in case of alarge capacity machine. However, the frequency may be chosen in a rangeof 10 to 100 Hz. The current I_(bc3) flowing between the "b" phase andthe "c" phase of the armature coil 1 is preferably about 10 to 20% ofthe rated current value. FIG. 15 summarizes measurement items andutilized measuring instruments for the measurement with respect to theabove-mentioned quadrature-axis. An order of the above threemeasurements can arbitrarily be chosen.

FIG. 16 shows an equivalent circuit of the synchronous machine in asituation wherein the rotor 2 is at the position shown in FIGS. 11, 12and 14. When the equivalent circuit is to be represented by mathematicalformula, the following equations can be obtained. ##EQU3##

In the above equations as a value of the armature frequency inductanceL_(l), for instance, the value obtained in the first example can beutilized. By putting known values to the above equations, the twoquadrature-axis unsaturated inductances, that is, the quadrature-axisdamper leakage inductance L_(kq) and the quadrature-axis armaturereaction inductance L_(aq) can be obtained.

In this way, according to Examples 1 and 2, the direct-axis unsaturatedinductances and the quadrature-axis unsaturated inductances can beobtained under the unified theory. The respective measurementsconcerning the direct-axis unsaturated inductances can be performed in asteady state, thereby preventing generation of errors accompanied byreading the timewisely variable data. Furthermore, persons for themeasurement are accustomed to the measurements of the no-load saturationcharacteristic and the three-phase short-circuit characteristic, sincethese are performed normally in all the synchronous machines.Accordingly, there is no performing difficulty and the measurements withhigh accuracy can be expected.

The measurements of the direct-axis inductances with the open-circuitfield and the direct-axis inductances with the short-circuit field bythe direct-axis Dalton-Cameron method, can be performed in a statewherein the synchronous machine is stationary. Therefore, there islittle performing difficulty and little concern of generating themeasurement errors due to a variation in a revolution number and anerror in the revolution number.

Furthermore, the respective measurements concerning the quadrature-axisunsaturated inductances can be performed in a situation wherein thesynchronous machine is stationally. Therefore, there is littleperforming difficulty and little concern of generating the measurementerrors due to a variation in a revolution number or an error in therevolution number.

As stated above, according to the first aspect of the present invention,in the measurement method of the unsaturated inductances of theequivalent circuit of the synchronous machine, the simultaneousequations concerning the equivalent circuit are solved by measuring theno-load saturation characteristic, by measuring the three-phaseshort-circuit characteristic and by measuring the direct-axisinductances in the predetermined positional relationship between thearmature and field by the direct-axis Dalton-Cameron method.Accordingly, the values of the inductances of the respective elementsconstituting the direct-axis equivalent circuit can be measured withhigh accuracy, and the optimum values of the motor constants to be setin the control device of the vector control can be obtained.

Furthermore, according to the second aspect of the present invention,the calculating equations concerning the equivalent circuit are solvedby using the respective values obtained by measuring the armatureresistance, by measuring the time constant of the quadrature-axisarmature with damper in the predetermined positional relationshipbetween the armature and the field, and by measuring the quadrature-axisinductances in the predetermined positional relationship between thearmature and field by the quadrature-axis Dalton-Cameron method.Therefore, the values of the inductances of the respective elementsconstituting the quadrature-axis equivalent circuit can be measured withhigh accuracy, and the optimum values of the motor constants to be setto the control device in the vector control, can be obtained.

Furthermore, the methods both in the first and second aspects of thepresent invention, can be performed at a time point wherein thesynchronous machine is integrated in a factory and at a stage of afactory single body test performed for the single body of thesynchronous machine. As a result, steps of adjusting wherein the controldevice for the vector control and the synchronous motor are combined,can be omitted, thereby reducing time and cost required beforestarting-up of the vector control system.

Obviously, numerous modifications and variations of the presentinvention are possible in light of the above teachings. It is thereforeto be understood that within the scope of the appended claims, theinvention may be practiced otherwise than as specifically describedherein.

What is claimed is:
 1. A method of measuring unsaturated inductances ofan equivalent circuit of a synchronous machine comprising:measuring anarmature resistance of a synchronous machine; measuring a time constantof an armature with damper under a quadrature-axis magnetomotive forceproduced by flowing current to an armature coil of the synchronousmachine when an armature and a field are in a positional relationship;measuring a current and a voltage of the armature when the armature andthe field are in said positional relationship by a quadrature-axisDalton-Cameron method; solving calculating equations concerning aquadrature-axis equivalent circuit of the synchronous machine by usingresults of the measuring the armature resistance, the measuring the timeconstant of the armature with damper under the quadrature-axismagnetomotive force and the measuring by the quadrature-axisDalton-Cameron method, thereby obtaining inductances of respectiveelements constituting the quadrature-axis equivalent circuit.